北京大学：《数学物理方法》精品课程电子教案（A类）第一部分 复变函数_第7讲 解析函数的Taylor展开

例71求e在=0点的 Taylor展开式 因为e在全平面解析,故可展开为

Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples ~7.1 ¦e z3z = 0:TaylorÐmª Ϗe z3²¡)Û§ŒÐm e z = X ∞ n=0 anz n |z| < ∞ qÏ ￾ e z
(n) = ez §¤± an = 1 n! ￾ e z
(n)    z=0 = 1 n! ∴ e z = X ∞ n=0 1 n! z n |z| < ∞ C. S. Wu 1Ôù )Û¼êTaylorÐm

例71求e在=0点的 Taylor展开式 因为e在全平面解析,故可展开为 ∑ 因(e

Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples ~7.1 ¦e z3z = 0:TaylorÐmª Ϗe z3²¡)Û§ŒÐm e z = X ∞ n=0 anz n |z| < ∞ qÏ ￾ e z
(n) = ez §¤± an = 1 n! ￾ e z
(n)    z=0 = 1 n! ∴ e z = X ∞ n=0 1 n! z n |z| < ∞ C. S. Wu 1Ôù )Û¼êTaylorÐm

例71求e在=0点的 Taylor展开式 因为e在全平面解析,故可展开为 ∑ 又因(e)(n)=e,所以 1 1

Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples ~7.1 ¦e z3z = 0:TaylorÐmª Ϗe z3²¡)Û§ŒÐm e z = X ∞ n=0 anz n |z| < ∞ qÏ ￾ e z
(n) = ez §¤± an = 1 n! ￾ e z
(n)    z=0 = 1 n! ∴ e z = X ∞ n=0 1 n! z n |z| < ∞ C. S. Wu 1Ôù )Û¼êTaylorÐm

例71求e在=0点的 Taylor展开式 因为e在全平面解析,故可展开为 ∑ 又因(e)(n)=e,所以 < n=0

Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples ~7.1 ¦e z3z = 0:TaylorÐmª Ϗe z3²¡)Û§ŒÐm e z = X ∞ n=0 anz n |z| < ∞ qÏ ￾ e z
(n) = ez §¤± an = 1 n! ￾ e z
(n)    z=0 = 1 n! ∴ e z = X ∞ n=0 1 n! z n |z| < ∞ C. S. Wu 1Ôù )Û¼êTaylorÐm

讲授要点 O Taylor,展开 展开定理 讨论 基本函数展开式 Tavion展开举例 级数乘法与待定系数法 多值函数的 avlon展开 。在无穷远点的 Taylor展开 ③解析函数的唯一性 解析函数零点的孤立性 。解析函数的唯一性

Expansion in Taylor Series Taylor Expansion: Examples Identity Theorem for Analytic Functions Theorem (Taylor) Discussions & Remarks Illustrative Examples ùLJ: 1 TaylorÐm Ðm½n ?Ø Ä¼êÐmª 2 TaylorÐmÞ~ ?ê¦{†½Xê{ õŠ¼êTaylorÐm 3á:TaylorÐm 3 )Û¼ê5 )Û¼ê":á5 )Û¼ê5 C. S. Wu 1Ôù )Û¼êTaylorÐm